JEE Advanced: harder problems, the same patient method

1. 1.General

   Units and dimensions, dimensional analysis · Least count and significant figures · Methods of measurement and error analysis · Vernier callipers and screw gauge · Determination of g using simple pendulum · Young's modulus by elasticity experiment · Surface tension of water by capillary rise · Specific heat of a liquid using calorimeter · Focal length of concave mirror and convex lens by u-v method · Speed of sound using resonance column · Verification of Ohm's law · Specific resistance using meter bridge and post office box

2. 2.Mechanics

   Kinematics in one and two dimensions · Projectiles · Uniform circular motion · Relative velocity · Newton's laws of motion · Inertial and uniformly accelerated frames of reference · Static and dynamic friction · Kinetic and potential energy · Work and power · Conservation of linear momentum and mechanical energy · Systems of particles, centre of mass and its motion · Impulse · Elastic and inelastic collisions · Rigid body and moment of inertia · Parallel and perpendicular axes theorems · Moment of inertia of uniform bodies · Angular momentum and torque · Conservation of angular momentum · Dynamics of rigid bodies with fixed axis of rotation · Rolling without slipping · Equilibrium of rigid bodies · Collision of point masses with rigid bodies · Forced and damped oscillation, resonance · Linear and angular simple harmonic motions · Hooke's law and Young's modulus · Law of gravitation, gravitational potential and field · Acceleration due to gravity · Kepler's law and geostationary orbits · Motion of planets and satellites in circular orbits · Escape velocity · Pressure in a fluid, Pascal's law and buoyancy · Surface energy, surface tension and capillary rise · Viscosity, Stokes' law and terminal velocity · Modulus of rigidity and bulk modulus · Streamline flow, equation of continuity and Bernoulli's theorem · Wave motion: longitudinal and transverse waves · Superposition, progressive and stationary waves · Vibration of strings and air columns, resonance and beats · Speed of sound in gases · Doppler effect in sound

3. 3.Thermal Physics

   Thermal expansion of solids, liquids and gases · Calorimetry and latent heat · Heat conduction in one dimension · Convection and radiation · Newton's law of cooling · Ideal gas laws · Specific heats Cv and Cp of gases · Isothermal and adiabatic processes, bulk modulus of gases · Equivalence of heat and work · First law of thermodynamics for ideal gases · Second law, reversible and irreversible processes · Carnot engine and its efficiency · Blackbody radiation and Kirchhoff's law · Wien's displacement law and Stefan's law

4. 4.Electricity and Magnetism

   Coulomb's law · Electric field and potential · Potential energy of point charges and dipoles · Electric field lines and flux · Gauss's law and its applications · Capacitance and parallel plate capacitor with dielectrics · Capacitors in series and parallel, energy stored · Electric current and Ohm's law · Series and parallel resistances and cells · Kirchhoff's laws and applications · Heating effect of current · Biot-Savart law and Ampere's law · Magnetic field of straight wire, circular coil and solenoid · Force on a moving charge and current-carrying wire · Magnetic moment of a current loop · Moving coil galvanometer, voltmeter and ammeter · Faraday's law and Lenz's law · Self and mutual inductance · RC, LR, LC and LCR circuits with d.c. and a.c. sources

5. 5.Electromagnetic Waves

   Electromagnetic waves and their characteristics · Electromagnetic spectrum and uses

6. 6.Optics

   Rectilinear propagation of light · Reflection and refraction at plane and spherical surfaces · Total internal reflection · Deviation and dispersion by a prism · Thin lenses and combinations of mirrors and lenses · Magnification · Huygens' principle · Young's double slit experiment · Diffraction due to a single slit · Polarization, Brewster's law and Polaroids

7. 7.Modern Physics

   Atomic nucleus and alpha, beta, gamma radiations · Law of radioactive decay and decay constant · Half-life and mean life · Binding energy and its calculation · Fission and fusion and energy calculations · Photoelectric effect · Bohr's theory of hydrogen-like atoms · Characteristic and continuous X-rays, Moseley's law · de Broglie wavelength of matter waves

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1. 1.General Topics

   Concept of atoms and molecules · Dalton's atomic theory · Mole concept · Chemical formulae and balanced equations · Stoichiometry of redox, neutralisation and displacement reactions · Mole fraction, molarity, molality and normality

2. 2.States of Matter: Gases and Liquids

   Gas laws and ideal gas equation · Absolute scale of temperature · Deviation from ideality and van der Waals equation · Kinetic theory of gases · Average, root mean square and most probable velocities · Law of partial pressures · Diffusion of gases · Intermolecular interactions and their effects · Liquids: vapour pressure, surface tension and viscosity

3. 3.Atomic Structure

   Bohr model and spectrum of hydrogen atom · Wave-particle duality and de Broglie hypothesis · Uncertainty principle · Quantum mechanical picture of hydrogen atom · Quantum numbers, wave function and probability density · Shapes of s, p and d orbitals · Aufbau principle, Pauli's exclusion principle and Hund's rule

4. 4.Chemical Bonding and Molecular Structure

   Orbital overlap and covalent bond · Hybridisation involving s, p and d orbitals · MO energy diagrams for homonuclear diatomic species · Hydrogen bond · Polarity in molecules and dipole moment · VSEPR model and shapes of molecules

5. 5.Chemical Thermodynamics

   Intensive and extensive properties, state functions · First law: internal energy, work and heat · Enthalpy, heat capacity and standard state · Hess's law · Enthalpy of reaction, fusion and vaporization · Lattice enthalpy · Second law and entropy · Gibbs energy · Criteria of equilibrium and spontaneity

6. 6.Chemical and Ionic Equilibrium

   Law of mass action · Significance of Gibbs energy change in equilibrium · Equilibrium constants Kp and Kc and reaction quotient · Le Chatelier's principle · Solubility product and its applications · Common ion effect · pH and buffer solutions · Bronsted and Lewis acids and bases · Hydrolysis of salts

7. 7.Electrochemistry

   Electrochemical cells and cell reactions · Standard electrode potentials · Electrochemical work and Nernst equation · Electrochemical series and emf of galvanic cells · Faraday's laws of electrolysis · Specific, equivalent and molar conductivity · Kohlrausch's law · Primary and secondary batteries, fuel cells · Corrosion

8. 8.Chemical Kinetics

   Rates of chemical reactions · Order and molecularity · Rate law, rate constant and half-life · Rate expressions for zero and first order reactions · Arrhenius equation and activation energy · Homogeneous and heterogeneous catalysis · Enzyme catalysis and its mechanism

9. 9.Solid State

   Classification of solids and crystalline state · Seven crystal systems · Close packed structures · Packing in fcc, bcc and hcp lattices · Nearest neighbours, ionic radii and radius ratio · Point defects

10. 10.Solutions

    Henry's law · Raoult's law and ideal solutions · Lowering of vapour pressure · Elevation of boiling point and depression of freezing point · Osmotic pressure · van't Hoff factor

11. 11.Surface Chemistry

    Physisorption and chemisorption · Freundlich adsorption isotherm · Colloids: types, preparation and properties · Emulsions, surfactants and micelles

12. 12.Classification of Elements and Periodicity in Properties

    Modern periodic law and periodic table · Electronic configuration of elements · Trends in atomic and ionic radius · Ionization enthalpy and electron gain enthalpy · Valence, oxidation states and electronegativity · Chemical reactivity

13. 13.Hydrogen

    Position, occurrence and isotopes of hydrogen · Preparation, properties and uses of hydrogen · Ionic, covalent and interstitial hydrides · Water and heavy water · Hydrogen peroxide · Hydrogen as a fuel

14. 14.s-Block Elements

    Reactivity of alkali and alkaline earth metals · Reducing nature and solutions in liquid ammonia · Oxides, hydroxides, halides and oxoacid salts · Anomalous behaviour of lithium and beryllium · Compounds of sodium · Compounds of calcium

15. 15.p-Block Elements

    Oxidation states and reactivity trends of groups 13-17 · Anomalous properties of B, C, N, O and F · Group 13: borax, boric acid, diborane, BF3, AlCl3 and alums · Group 14: allotropes of carbon, CO, CO2, silicones, silicates, zeolites · Group 15: nitrogen, ammonia, nitric acid, phosphine, phosphorus halides · Oxides of nitrogen and oxoacids of phosphorus · Group 16: dioxygen, ozone, SO2, sulphuric acid, oxoacids of sulphur · Group 17: chlorine, HCl, interhalogens, oxoacids, bleaching powder · Group 18: properties and xenon compounds

16. 16.d-Block Elements

    Oxidation states and their stability · Standard electrode potentials · Interstitial compounds and alloys · Catalytic properties and applications · Oxoanions of chromium and manganese

17. 17.f-Block Elements

    Lanthanoid and actinoid contractions · Oxidation states · General characteristics

18. 18.Coordination Compounds

    Werner's theory · Nomenclature · Cis-trans and ionization isomerism · Hybridization and geometries · Bonding: VBT and CFT · Spin-only magnetic properties and colour · Ligands and spectrochemical series · Stability, importance and applications · Metal carbonyls

19. 19.Isolation of Metals

    Metal ores and their concentration · Thermodynamic principles of metallurgy · Electrochemical principles of metallurgy · Cyanide process for silver and gold · Refining

20. 20.Principles of Qualitative Analysis

    Cations of groups I to V · Nitrate, halides, carbonate and bicarbonate · Sulphate and sulphide

21. 21.Environmental Chemistry

    Atmospheric pollution · Water pollution · Soil pollution and industrial waste · Strategies to control pollution · Green chemistry

22. 22.Basic Principles of Organic Chemistry

    Hybridisation of carbon, sigma and pi bonds · Shapes of simple organic molecules · Aromaticity · Structural and geometrical isomerism · Stereoisomers: enantiomers, diastereomers and meso · Empirical and molecular formulae by combustion · IUPAC nomenclature of organic molecules · Hydrogen bonding effects · Inductive, resonance and hyperconjugative effects · Acidity and basicity of organic compounds · Reactive intermediates from bond cleavage · Carbocations, carbanions and free radicals

23. 23.Alkanes

    Homologous series · Physical properties and effect of branching · Conformations of ethane and butane · Preparation from alkyl halides and carboxylic acids · Combustion, halogenation and oxidation

24. 24.Alkenes and Alkynes

    Physical properties · Preparation by elimination reactions · Acid catalysed hydration · Metal acetylides · Reactions of alkenes with KMnO4 and ozone · Reduction of alkenes and alkynes · Electrophilic addition of X2, HX and HOX · Effect of peroxide on addition reactions · Cyclic polymerization of alkynes

25. 25.Benzene

    Structure of benzene · Halogenation, nitration and sulphonation · Friedel-Crafts alkylation and acylation · Effect of directing groups

26. 26.Phenols

    Physical properties and preparation · Electrophilic substitution of phenol · Reimer-Tiemann and Kolbe reactions · Esterification and etherification · Aspirin synthesis · Oxidation and reduction of phenol

27. 27.Alkyl Halides

    Rearrangement of alkyl carbocations · Grignard reactions · Nucleophilic substitution and stereochemistry

28. 28.Alcohols

    Physical properties · Esterification and dehydration · Reactions with sodium, phosphorus halides, Lucas reagent and SOCl2 · Conversion to aldehydes, ketones and carboxylic acids

29. 29.Ethers

    Williamson's synthesis · C-O bond cleavage reactions

30. 30.Aldehydes and Ketones

    Preparation from acid chlorides, nitriles and esters · Benzaldehyde from toluene and benzene · Oxidation and reduction · Oxime and hydrazone formation · Aldol condensation and Cannizzaro reaction · Haloform reaction · Nucleophilic addition with RMgX, NaHSO3, HCN, alcohol and amine

31. 31.Carboxylic Acids

    Physical properties · Preparation from nitriles, Grignard reagents, esters and amides · Benzoic acid from alkylbenzenes · Reduction and halogenation · Formation of esters, acid chlorides and amides

32. 32.Amines

    Preparation from nitro compounds, nitriles and amides · Hoffmann bromamide degradation · Gabriel phthalimide synthesis · Reaction with nitrous acid · Azo coupling of diazonium salts · Sandmeyer and related reactions · Carbylamine reaction and Hinsberg test · Alkylation and acylation

33. 33.Haloarenes

    Fittig and Wurtz-Fittig reactions · Nucleophilic aromatic substitution

34. 34.Biomolecules

    Classification of carbohydrates · Glucose and sucrose · Oxidation and reduction of carbohydrates · Glycosides and hydrolysis of disaccharides · Anomers · Amino acids and peptide linkage · Primary and secondary structure of peptides · Fibrous and globular proteins · Composition and structure of DNA and RNA

35. 35.Polymers

    Addition and condensation polymerization · Homopolymers and copolymers · Natural rubber and cellulose · Nylon, Teflon, Bakelite and PVC · Biodegradable polymers · Applications of polymers

36. 36.Chemistry in Everyday Life

    Drug-target interaction · Antacids, antihistamines and tranquilizers · Analgesics, antimicrobials and antifertility drugs · Artificial sweeteners · Soaps, detergents and cleansing action

37. 37.Practical Organic Chemistry

    Detection of N, S and halogens · Detection of hydroxyl and carbonyl groups · Detection of carboxyl, amino and nitro groups

Official sources:jeeadv.ac.injeeadv.ac.in

1. 1.Sets, Relations and Functions

   Sets and their representations · Empty, finite and infinite sets · Algebra of sets · Intersection, complement, difference and symmetric difference · De Morgan's laws · Cartesian product and ordered pairs · Relations, domain and codomain · Equivalence relation · Functions as mappings: domain, codomain and range · Invertible functions · Even and odd functions · Into, onto and one-to-one functions · Special functions · Sum, difference, product and composition of functions

2. 2.Algebra

   Algebra of complex numbers · Conjugation and polar representation · Modulus, principal argument and triangle inequality · Cube roots of unity · Geometric interpretations of complex numbers · Fundamental theorem of algebra · Quadratic equations with real coefficients · Relations between roots and coefficients · Symmetric functions of roots · Arithmetic and geometric progressions and means · Infinite geometric series · Sums of natural numbers, squares and cubes · Logarithms and their properties · Permutations and combinations · Binomial theorem for a positive integral index · Properties of binomial coefficients

3. 3.Matrices

   Equality, addition and scalar multiplication of matrices · Product and transpose of matrices · Elementary row and column transformations · Determinant of order up to three · Adjoint and inverse of a matrix · Diagonal, symmetric and skew-symmetric matrices · Simultaneous linear equations in two or three variables

4. 4.Probability and Statistics

   Random experiment, sample space and events · Addition and multiplication rules · Conditional probability and independence · Total probability and Bayes' theorem · Probability using permutations and combinations · Measures of central tendency · Mean deviation, standard deviation and variance · Frequency distributions with same mean, different variance · Random variable, its mean and variance

5. 5.Trigonometry

   Trigonometric functions, periodicity and graphs · Addition and subtraction formulae · Multiple and sub-multiple angle formulae · General solution of trigonometric equations · Inverse trigonometric functions

6. 6.Analytical Geometry

   Cartesian coordinates, distance and section formulae · Shift of origin · Straight line in various forms · Angle between lines and distance of a point from a line · Lines through intersection of two lines · Angle bisectors and concurrency of lines · Centroid, orthocentre, incentre and circumcentre · Circle: equations, tangent, normal and chord · Parametric equations of a circle · Intersection of circles and lines · Family of circles through intersection points · Parabola, ellipse and hyperbola in standard form · Foci, directrices and eccentricity · Parametric equations, tangents and normals of conics · Locus problems · 3D: distance, direction cosines and direction ratios · 3D: equation of a straight line in space · Skew lines and shortest distance · Equation of a plane and distance of a point from it · Angles between lines, planes, and a line and a plane · Coplanar lines

7. 7.Differential Calculus

   Limit of a function · Continuity of a function · Limits and continuity of sum, difference, product and quotient · L'Hospital rule · Continuity of composite functions · Intermediate value property · Derivative of sum, difference, product and quotient · Chain rule · Derivatives of standard functions · Tangents and normals · Increasing and decreasing functions · Derivatives of order two · Maximum and minimum values · Rolle's theorem and Lagrange's mean value theorem · Derivatives of implicit functions · Geometric interpretation of derivatives

8. 8.Integral Calculus

   Integration as inverse of differentiation · Indefinite integrals of standard functions · Definite integral as limit of sums · Properties of definite integrals · Fundamental theorem of integral calculus · Integration by parts · Integration by substitution and partial fractions · Areas bounded by simple curves · Formation of ordinary differential equations · Homogeneous differential equations of first order · Separation of variables method · Linear first order differential equations

9. 9.Vectors

   Addition of vectors and scalar multiplication · Dot and cross products · Scalar and vector triple products · Geometrical interpretations

Official sources:jeeadv.ac.injeeadv.ac.in